Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C157 · Schur multiplier (H2) = C25 |
| direct product | C2×#131×C157 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C157 | C22 |
| commutator | C2 | C23×C4×C157 |
| Frattini, cosocle | C4 | C24×C157 |
| socle | C22×C157 | C22×C4 |
| prime radical | C2×#41×C157 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C157 ◁ G | |
266 conjugacy classes of subgroups.
6280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1757×C157, #1764×C157, #1765×C157, … |
| maximal normal subgroup of | #1757×C157, #1764×C157, #1765×C157, … |
| maximal quotient of | C2×#405×C157, C4×#131×C157, C2×#408×C157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 248);